Stochastic Production Simulation Research Articles

The research of declared primary frequency capacity and control strategy for electrical fused magnesium furnace load

As a potential control resource of the load side, fused magnesium load can effectively make up for the loss of the primary frequency modulation capacity of the system, in which the conventional units are replaced by new energy sources. However, the capacity of fused magnesium load is closely related to the operating condition and changes dynamically. It is necessary to accurately characterize its capacity and determine the optimal declared capacity of participating in frequency modulation service. According to the technical regulations of primary frequency modulation service, the basic principle is presented, which the electric molten magnesium load participates in primary frequency modulation control in the case of lack of large power. Considering the risk of reward and punishment, the optimal reporting capacity optimization model is constructed. Taking the year as the time scale, a stochastic production simulation method involving primary frequency modulation was proposed. According to its operating characteristics, a real-time control strategy involving primary frequency modulation is designed. Simulation examples show that the proposed method can accurately simulate the production process of molten magnesium load, reasonably realize the operation control of molten magnesium load, and optimize the declared capacity considering the risk.

Optimization of declared capacity for electrical fused magnesia furnaces participating in primary frequency control

In the frequency response of the new power system, fused magnesium as a load side resource has great potential for frequency modulation. Due to the need to adapt to the medium and long term power market demand, the existing fused magnesium simulation methods which only take single ton energy consumption as the index are difficult to determine the declared capacity. Therefore, according to the requirement of annual time scale and the randomness of molten magnesium production process, a stochastic production simulation algorithm framework was designed to simulate the operation state of molten magnesium load. Based on the Markov chain Monte Carlo method and the idea of integer random distribution, the transition and duration of each state were simulated. According to the rule of two-step system, an optimization model for the declared capacity of fused magnesium was established, and the optimal declared capacity and enterprise income were solved by the ergodic optimization algorithm, so as to achieve the goal of frequency response on the load side. The simulation example shows that the proposed method can well characterize the production process of electrical fused magnesium load, calculate the optimal declared capacity for the scenario of power loss in the medium and long term market, which brings economic benefits to enterprises and provides fast frequency response resources for power grid.

Multi-time scale stochastic production simulation under VHVDC long-term contract trading electricity quantity constraint

A two-layer multi-time scale stochastic production simulation framework is constructed to account for the long-term contract electricity quantity of ultra-high voltage direct current (UHVDC) transmission. On the upper layer, based on the characteristics of load demand and renewable energy output extracted from the historical operating data, monthly and daily production simulation models are carried out considering the seasonal characteristics of hydropower during a high-water period and low-water period to optimize the distribution of contract electric quantity sending through UHVDC transmission in the target year or month. According to the DC transmission electric quantity optimized by the daily production simulation in the upper layer, together with the forecast scenario, the lower layer of the framework provides the optimization of day-ahead scheduling and intra-day rolling dispatch in the implementation process. The day-ahead dispatch optimization makes full use of the adjustment capability of transmission and optimizes the DC transmission electric quantity correction. Its compensation is based on the result of the daily production simulation, then the correction will be returned to the upper layer to restart the optimization of the remaining UHVDC contract electric quantity of the subsequent period and its distribution plan. Combined with the day-ahead DC transmission plan, the intra-day rolling optimization is carried out to adjust the output of the unit using more accurate forecasting scenarios. The distributionally robust optimization model is used in the lower layer to convert an uncertain problem into a deterministic quadratically constrained quadratic programming (QCQP) problem according to the form of an uncertain distribution set. Then the QCQP problem is further converted into a linear programming (LP) problem by using the reformulation linearization technique (RLT). A test system with the energy composition and distribution referring to a real provincial power grid in northwest China is established for verification. The results show that the proposed method can effectively improve the economics of system operation and the accommodation of renewable energy based on ensuring security.

Optimal Peak Shaving Analysis of Power Demand Response Considering Unit Uncertainty

With the increasingly prominent environmental problems and the promotion of the “double carbon” goal, the participation of demand-side response resources in load peak shaving and valley filling is of great significance to the development of the power industry. In this paper, based on the background that demand-side response is being rapidly developed in China, we firstly consider the uncertainty of generating units and the operating constraints of power system and units, and construct the day-ahead output model of generating units by using stochastic production simulation and day-ahead optimal scheduling. Then, based on this model, we consider the impact of demand response on system peak shaving and build a demand response power system optimal scheduling model with unit uncertainty. Finally, the power supply and demand of the IEEE30 node system on two typical days of peak shaving considering demand response are analysed by MATLAB, and the minimum service cost of demand response and the amount of pull-out limit are derived, which clarify the important role of demand response in the process of power system peak shaving.

Peak Shaving Analysis of Power Demand Response with Dual Uncertainty of Unit and Demand-Side Resources under Carbon Neutral Target

With the depletion of fossil energy and increasingly serious environmental problems, demand-side resources play an increasingly prominent role in peak shaving and valley filling, energy conservation, and emission reduction. Under the background of further promotion of the “double carbon” goal in China, considering the possible double uncertainty factors in the process of unit and demand response resources participating in the scheduling and the goal of minimum carbon emission, the uncertainty models of unit output and demand-side resource response are respectively constructed based on the sequential stochastic production simulation algorithm and the method of additional random variables. In the model, the influence of random forced outage on unit output and the uncertain influence of response deviation caused by the limitation of demand response resource information processing and response aging characteristics are considered, respectively. By analyzing the power supply and demand, considering demand response on two typical peak shaving days, the peak shaving cost, carbon emission reduction, and power limitation are obtained. An IEEE 30 bus 6-machine system example is used to verify the effectiveness of the dual uncertainty demand response model, which provides guidance for power dispatching decision-making.

Stochastic production simulation for generating capacity reliability evaluation in power systems with high renewable penetration

Stochastic production simulation for generating capacity reliability evaluation in power systems with high renewable penetration

Renewable energy integration capacity assessment in regional power grid based on an enhanced sequential production simulation

As the scale of renewable energy increases significantly, the renewable energy integration will gradually become the key issue in urgent need of a solution for Shaanxi power system. To tackle such a new situation, this study proposes an innovative method for accessing the renewable energy integration capacity of Shaanxi power system during the next ‘Five-Year Plan’ period. First, an in-depth study of the power demand, load characteristics, renewable energy as well as their output characteristics is performed. Then, the maximum wind and solar power integration capacity is simultaneously calculated based on an enhanced sequential stochastic production simulation in consideration of several boundary conditions of Shaanxi power system such as power supply, network constraints and future load. Finally, the influence of electric heating scale in Yulin region on the renewable energy integration capacity of Shaanxi power system is further studied. Through such analysis, this study attempts to provide decision support for a reasonable renewable energy development scale and power grid plan.

Optimal Spinning Reserve for Power System with Wind Integrated

This paper presents an evolutionary stochastic production simulation to solve the optimal spinning reserve configuration problem in power system with wind integrated. Equivalent load curve is generated with considering the wind power forecasting deviation and generation scheduling of hydropower plant in different water periods. The equivalent load duration curve (ELDC), redrawn from equivalent load curve is the core of stochastic production simulation which focuses on random outage of generator and load fluctuation. The optimal spinning reserve model is established around the reliability index Expected Energy Not Served (ENNS). The optimal scheduling of spinning reserve is reached while the cost of purchasing spinning reserve is equal to the outage loss. At last, results of the optimal spinning reserve model tested in Hainan power grid help reduce the costs of spinning reserve configuration.

Two-area power system costing by the cumulant method using available capacity distribution

This paper extends the cumulant method using available capacity distribution to evaluate the production costs of two-area power systems, in which the random characters of generating available capacity and the transmission capacity limit have been considered accurately. By means of the independence of both systems equivalent available capacity based on a chronological load curve, the single-variant cumulant and single-variant Gram-Charlier Series A approximation are adequate for the two-area production simulation. The method gives a new approach to stochastic production simulation for a two-area power system, and is easily extended to three-areas or multi-areas. Sample studies show favourable accuracy and efficiency results.

Sample size reduction in stochastic production simulation

A combined control variable and stratified sampling method is proposed for Monte Carlo production simulation. Using the production cost obtained from the load duration curve type simulation as the control variable, both the theory and a sample study suggest that the required (for an acceptable coefficient of variation) number of samples can be reduced by approximately a factor of 1000. In the example study, 8000 samples were replaced with 10 samples; in addition, the proposed method using the 10 samples produces an estimator of the mean production cost that has a much smaller variance than an estimator based on a traditional Monte Carlo study which uses 8000 samples. It is believed that this significant reduction in running time will enable chronological simulation to be used in a number of long range planning studies. The advantage of this method is additional insight into actual operation through chronological simulation as well as less bias (or systematic error). With this proposed method, it is believed that the computational time requirement of stochastic production cost simulation has been reduced to the point that its advantages outweigh its additional (over probabilistic simulation) running time.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A new method for stochastic production simulation in generation system with multiple hydro units

A novel method is presented for calculating loss of load probability, expected energy generation and production cost for units in a generating system with multiple hydro units. The method uses the equivalent load duration curve (ELDC) obtained by convolving the distributions of the original load and the forced outage power loss of all generators. Hydro units are scheduled on the ELDC according to their assigned energy and available capacity. Then the deconvolution procedure is performed to obtain a load duration curve for an equivalent system without hydro units. The expected energy of the thermal units is achieved by convolving the generating units in an economic merit order of loading.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Production Simulation for Power System Studies

Predicting expected generation for different power plants as well as the system's total expected production cost is an integral part of quantitative power system analyses. Numerous publications presenting exact as well as approximate methods of solving stochastic production simulation problem exist in the literature. However, there is no one publication where a comprehensive review of this extremely important topic is presented. Such a review is the subject of this paper.

Analytical Treatment of Hydro Units with Random Energy in Stochastic Production Simulation

Analytical Treatment of Hydro Units with Random Energy in Stochastic Production Simulation

Analytical Treatment of Hydro Units with Random Energy in Stochastic Production Simulation

The problem of simulating the production process in a hydrothermal system is addressed in a stochastic environment. A method is demonstrated to simulate the operation of a seasonal hydro unit with random energy in a stage-by-stage stochastic production simulation approach. The method can be extended to several independent units with minor adaptations.